It seems that I have misunderstood "logic" and its associated parts of speech! I think "logical" and "illogical" has some specific usages which is not associated with the words like "reasonable" or "rational"! (I have always used them as synoymous words.)
I wonder if you could help me to discover my possible missing points. I have made up a scenario! I need to know if using the word "logical" sounds idiomatic in my example or not? If not, then why?
Please assume that a student has missed several seasons in a course and after a while, he/she starts to attend their classes. When the teacher asks them aboutvthe reason of their absence for that long time, they just try to make up some fake reasons, but the teacher immediately notices that they are bringing up some implausible excuses to "justify themselves". As for this case and based on what you mentioned being "illegal" or "immoral", the teacher should be able to say some sentences using the "justification" family words like:
— This is not a logical justification.
— Your reasoning is not logical!
Note: let's say the student had raised some unreasonable and irrational excuses which did not sound logical to the teacher.